A defiant North Korea has issued a fiery response to Donald Trump, warning the US was "getting on its nerves" and that Kim Jong-un was currently studying a plan of attack.

The DPRK also revealed further details of an operational plan for a medium-to-long-range ballistic missile attack on the island of Guam.

The North Korean Strategic Force of the Korean People's army warning comes after the US President said any threats from the DPRK would be met with "fire and fury".

Citing General Kim Rak Gyom, commander of the Strategic Force of the Korean People's Army, North Korea's state news agency KCNA, said Kim was "seriously examining the plan for an enveloping strike at Guam through simultaneous fire of four Hwasong-12 intermediate-range strategic ballistic rockets in order to interdict the enemy forces on major military bases on Guam and to signal a crucial warning to the US."

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Gyom also said the North would finalise a plan by mid-August involving mid-range missiles hitting waters 30 to 40 kilometres away from the island.

North Korea remains angered after the US flew their B-1B bombers over the peninsula twice in the past week, NK News reported.

Guam is home to two major bases, the Andersen air force Base in the north and Naval Base Guam in the south with 7000 soldiers and more than 160,000 people.

The KPA statement said it was "now carefully examining the operational plan for making an enveloping fire at the areas around Guam" using the Hwasong-12 ballistic missile.

Nuclear-armed North Korea's ballistic missile. Photo/AP
Nuclear-armed North Korea's ballistic missile. Photo/AP

North Korea said the plan will be analysed by the Supreme Command and will be put into force as soon as leader Kim Jong-un makes a decision.

"The execution of this plan will offer an occasion for the Yankees to be the first to experience the might of the strategic weapons of the DPRK," the KPA statement reads.

"The US should clearly face up to the fact that the ballistic rockets of the Strategic Force of the KPA are now on constant standby, facing the Pacific Ocean and pay deep attention to their azimuth angle for launch."

The comments come after Donald Trump warned the US nuclear arsenal is "stronger and more powerful" than North Korea's.

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It also comes after US intelligence found North Korea had produced a nuclear warhead small enough to fit inside a ballistic missile, sidelining many experts who believe this move was some way off.

North Korea has rejected the President's warning, dismissing his comments as a "load of nonsense".

It said "only absolute force" can work on someone as "bereft of reason" as Trump and added it will "keep closely watching the speech and behaviour of the US."

Meanwhile US Defense Secretary Jim Mattis issued his own sharp threat to North Korea, and said the regime should cease any consideration of actions that would "lead to the end of its regime and the destruction of its people."

Mr Mattis said any action by North Korea would be grossly overmatched by the US, and that Pyongyang would lose any arms race or conflict it started.

He also said that while the US is pursuing diplomatic solutions, the combined military power of America and its allies is the most robust on Earth.

Naval Base Guam is the home port for four nuclear-powered fast attack submarines and two submarine tenders.